Question

2kg of a radioactive sample decays into 0.25 kg in 12 years. thw half life period of the sample is

Answer 1

Half life;

The half life of a radioactive substance, is the time taken or required by a radioactive isotope or substance for the value of its quantity to fall by a half. 

For example; if the half life of a 4 kg radioactive substance is 1 hour, then after 1 hour its mass will be 2 kg, after another it will be 1 kg...and so on.

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We can use the formula:

(1/2)ⁿ  ₓ original quantity = final quantity(at time t)

to the find the number of half lives in the question above.

Where n = the number of half lives

Therefore  (1/2)ⁿ ₓ 12kg = 0.25 kg
                   (1/2)ⁿ = 0.25/12
                   (1/2)ⁿ = 0.02083

You can solve the equation using logarithms, that is incorporate log to base 10

                     log(1/2)ⁿ = log 0.02083

                       n log 1/2 = log 0.02083

                      n = log 0.02083/log 0.5

                      n =5.58496250072
             round off to the nearest whole number 6
Therefore the number of half lives in the 12 years were 6 in total

Find the length of one half life:   12/6

                                               = 2

The half life of this substance is thus approximately 2 years.